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IG-VAE: Generative Modeling of Immunoglobulin Proteins by Direct bioRxiv preprint doi: https://doi.org/10.1101/2020.08.07.242347; this version posted August 10, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. IG-VAE: GENERATIVE MODELING OF IMMUNOGLOBULIN PROTEINS BY DIRECT 3D COORDINATE GENERATION Raphael R. Eguchi Namrata Anand Christian A. Choe Department of Biochemistry Department of Bioengineering Department of Bioengineering Stanford University Stanford University Stanford University [email protected] [email protected] [email protected] Po-Ssu Huang Department of Bioengineering Stanford University [email protected] ABSTRACT While deep learning models have seen increasing applications in protein science, few have been implemented for protein backbone generation—an important task in structure-based problems such as active site and interface design. We present a new approach to building class-specific backbones, using a variational auto-encoder to directly generate the 3D coordinates of immunoglobulins. Our model is torsion- and distance-aware, learns a high-resolution embedding of the dataset, and generates novel, high-quality structures compatible with existing design tools. We show that the Ig-VAE can be used to create a computational model of a SARS-CoV2-RBD binder via latent space sampling. We further demonstrate that the model’s generative prior is a powerful tool for guiding computational protein design, motivating a new paradigm under which backbone design is solved as constrained optimization problem in the latent space of a generative model. 1 Introduction Over the past two decades, the field of protein design has made steady progress, with new computational methods providing novel solutions to challenging problems such as enzyme catalysis, viral inhibition, de novo structure generation and more[1, 2, 3, 4, 5, 6, 7, 8, 9]. Building on the improvements in force field accuracy and conceptual advancements in understanding structural engineering principles, computational protein design is seemingly ready to take on any engineering challenge. However, designs created computationally rarely match the performance of variants derived from directed evolution experiments; there is still much room for improvement. While design force fields are known to be imperfect, a major limitation of computational design also stems from the difficulty in modeling backbone flexibility, specifically, movements in loops and the relative geometries of the structural elements in the protein. When comparing structural changes between pre- and post-evolution structures, we often find that the polypeptide chain responds to sequence changes in ways not predictable by the design algorithm. This is because current methods, such as Rosetta[10], tend to restrict backbone conformations to local energy minima. While this issue is usually addressed by sampling backbone torsional angles from known fragments, such a stochastic optimization process is discrete, sparse, time-consuming, and rarely uncovers the true ground state. To address this fundamental challenge in modeling protein structure, we explore the use of deep neural networks to infer a continuous structural space in which we can smoothly interpolate between different backbone conformations. In doing so we seek to capture elements of backbone motility that are otherwise difficult to reflect in rigid body design. We focus on the task of antibody design, as it harbors many challenges common across different protein design problems and is of significant practical importance: applications of antibodies have been found in every sector of biotechnology, from diagnostic procedures to immunotherapy. bioRxiv preprint doi: https://doi.org/10.1101/2020.08.07.242347; this version posted August 10, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. With recent advances in deep learning technology, machine learning tools have seen increasing applications in protein science, with deep neural networks being applied to tasks such as sequence design[11], fold recognition[12], binding site prediction[13], and structure prediction[14, 15]. Generative models, which approximate the distributions of the data they are trained on, have garnered interest as a data-driven way to create novel proteins. Unfortunately, the majority of protein-generators create 1D amino acid sequences[16, 17] making them unsuitable for problems that require structure-based solutions such as designing protein-protein interfaces. Very few machine learning models have been implemented for protein backbone generation[18, 19], and none of the reported methods produce structures comparable in quality to those of experimentally validated tools such as RosettaRemodel[20]. Previously, our group was the first to report a Generative Adversarial Network (GAN) that generated 64-residue backbones that could serve as templates for de novo design[19]. This prior work focused on unconditioned structure generation via a distance matrix representation, and 3D coordinates were recovered using a convex optimization algorithm[19] or a learned coordinate recovery module[21]. Despite its novelty, the GAN method is accompanied by certain difficulties. The generated distance constraints are not guaranteed to be Euclidean-valid, and thus it is not possible to recover 3D coordinates that perfectly satisfy the generated constraints. We found that the quality of the recovered backbone torsions could often be degraded due to inconsistencies or errors in the generated distance constraints, leading to loss of important biochemical features, such as hydrogen-bonding. Moreover, since the GAN is trained on peptide fragments, we are not guaranteed to sample constraints for globular structures that can eventually fold. In this study, we use a variational autoencoder (VAE)[22] to perform direct 3D coordinate generation of full-atom protein backbones, circumventing the need to recover coordinates from pairwise distance constraints, and also avoiding the problem of distance matrix validity[23]. Using a coordinate representation has allowed us to make our model torsion-aware, significantly improving the quality of the generated backbones. Importantly, our model motivates a conceptually new way of solving protein design problems. Because the Ig-VAE generates coordinates directly, all of its outputs are fully differentiable through the coordinate representation. This allows us to use the generative prior to constrain structure generation with any differentiable coordinate-based heuristic, such as Rosetta energy, backbone shape constraints, packing metrics, and more. By optimizing a structure in the VAE latent space, designers are able to specify a set of desired structural features while the model creates the rest of the molecule. As an example of this approach, we use the Ig-VAE to perform constrained loop generation, towards epitope-specific antibody design. Our technology ultimately paves the way for a novel approach to protein design in which backbone construction is solved via constrained optimization in the latent space of a generative model. In contrast to conventional methods[20, 24], we term this approach “generative design.” Figure 1: VAE Training Scheme. The flow of data is shown with black arrows, and losses are shown in blue. First, Ramachandran angles and distance matrices are computed from the full-atom backbone coordinates of a training example. The distance matrix is passed to the encoder network (E), which generates a latent embedding that is passed to the decoder network (D). The decoder directly generates coordinates in 3D space, from which the reconstructed Ramachandran angles and distance matrix are computed. Errors from both the angles and distance matrix are back-propagated through the 3D coordinate representation to the encoder and decoder. Note that both the torsion and distance matrix losses are rotationally and translationally invariant, and that the coordinates of the training example are never seen by the model. The shown data are real inputs and outputs of the VAE for the immunoglobulin chain in PDB:4YXH(L). 2 bioRxiv preprint doi: https://doi.org/10.1101/2020.08.07.242347; this version posted August 10, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 2 Methods 2.1 Dataset All training data were collected from the antibody structure database AbDb[25]. Domains that were missing residues were excluded, and sequence-redundant structures were included to allow the network to learn small backbone fluctuations. The final training set is comprised of 10768 immunoglobulins spanning 4154 non-sequence-redundant structures, including single-domain antibodies. The training set covers close to 100% of the AbDb database. Structures in the dataset vary in length from 89 to 138 residues, with most falling between 114 and 130. Since the input of our model was fixed at 128 residues (512 atoms), structures larger than 128 were center-cropped. Structures smaller than 128 were “structurally padded” by using RosettaRemodel to append dummy residues to the N and C termini. The reconstruction loss of the padded regions was down-weighted over the course of training (see Supplemental Methods). We found that the structural padding step led to slight improvements in local bond geometries at the terminal
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